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SageMath
E = EllipticCurve("j1")
E.isogeny_class()
Elliptic curves in class 30345.j
sage: E.isogeny_class().curves
LMFDB label | Cremona label | Weierstrass coefficients | j-invariant | Discriminant | Torsion structure | Modular degree | Faltings height | Optimality |
---|---|---|---|---|---|---|---|---|
30345.j1 | 30345u2 | \([1, 0, 0, -60696, -2816835]\) | \(208527857/91875\) | \(10895261153161875\) | \([2]\) | \(208896\) | \(1.7731\) | |
30345.j2 | 30345u1 | \([1, 0, 0, 12999, -325944]\) | \(2048383/1575\) | \(-186775905482775\) | \([2]\) | \(104448\) | \(1.4265\) | \(\Gamma_0(N)\)-optimal |
Rank
sage: E.rank()
The elliptic curves in class 30345.j have rank \(0\).
Complex multiplication
The elliptic curves in class 30345.j do not have complex multiplication.Modular form 30345.2.a.j
sage: E.q_eigenform(10)
Isogeny matrix
sage: E.isogeny_class().matrix()
The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.
\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)
Isogeny graph
sage: E.isogeny_graph().plot(edge_labels=True)
The vertices are labelled with LMFDB labels.